Basic Factorial Designs Overview

A factorial design refers to how/which factor level combinations are chosen for inclusion in the study.

Basic Factorial designs have some key characteristics in common, notably:

• For studies with more than one factor, factors levels are created by crossing factors¹

• Treatments are assigned to subjects (a.k.a. experimental units) completely at random²

To assign something completely at random means that each experimental unit has a known and equal chance of being selected for a particular treatment and that no other considerations are taken into account when making treatment assignments.

The decomposition and formulas presented for each of the specific designs assumes the design is balanced, meaning each factor level combination has the same number of observations. In the case of unbalanced designs, formulas would need to be adjusted to account for the differences. Additional explanation of how to approach analysis for unbalanced data is found under broad topics>unbalanced.

Footnotes

1. Factorial crossing is defined in BF[2] and in the Factor Structure page.

2. Once the factor level combinations are decided upon using factorial crossing, there are multiple ways to perform the random assignment of experimental units to factor levels. In this book though, all of the BF models will be treated as using completely randomized assignment. Strategies such as blocking and repeated measures are treated as separate designs.